Question

How do you factor `-x^2+3x+4`?

Answer 1

See a solution process below:

Explanation:

Because the `x^2` coefficient is `-1` we know the coefficient for one the `x` terms in the factor will also be `1` and the other a `-1`:

`(x )(-x )`

Because the constant is a positive and the coefficient for the `x` term is a positive, then the sign for the constants in the factors will both be positive::

`(x + )(-x + )`

Now we need to determine the factors which multiply to 4 and also add to 3:

`1 xx 4 = 4`; `-1 + 4 = 3` <- this IS the factor

`(x + 1)(-x + 4)`